The party of new Prime Minister Alexis Tsipras swept to office on the back of Greeks angry at Europe-imposed austerity. But Syriza may find that living up to its promise to renegotiate Europe's terms is a difficult, if not impossible, task.

The EU took a tough tone towards Greece after the radical left party Syriza stormed to victory in elections, warning that Athens' place in the eurozone depended on it honouring agreements on debt and austerity.

Athens — For hundreds of thousands of Greeks who voted on Sunday – people like Golfo Roussou, a widow getting food handouts, or Stavros Davos, an unemployed professional who squeaks by on odd jobs – business as usual simply could not continue.

It was their cry for change and "dignity" that sparked a landslide victory for left-wing Syriza candidate Alexis Tsipras – and a watershed moment for Greece and the whole of Europe.

Mr. Tsipras's victory threatens to usher in a period of high-stakes unpredictability on the Continent – especially as the ranks of austerity critics swell on both the right and left. Tsipras has promised to renegotiate terms of Greece’s bailout package, and to end harsh austerity measures imposed on Greece after it faced a historic collapse in 2009. But European leaders – mindful of their electorates, who resent having had to bail out debt-ridden countries like Greece – have insisted those terms must stand.

Delicate negotiations in the coming weeks will test whether that gap can be bridged. Any miscalculation could end up with an outcome no one wants: a Greek exit from the eurozone. But it is difficult to see a solution that both Greeks and pro-austerity leaders in Europe would agree to and that would still satisfy a beaten-down Greek population expectant that Europe is finally about to listen.

“They have to understand that it is unbearable here,” says Mania Papadimitriou, a Syriza lawmaker and an actress. For all of the uncertainty ahead, she says, there is one thing that Greeks have made clear: “I’m sure they do not want to go back to yesterday.”

A story of loss

Syriza won in a landslide last night, falling just one seat short of an absolute majority in the parliament, according to official projections. Tsipras was sworn in as the new prime minister today, after Syriza formed a coalition with the anti-austerity, right-wing Greek Independents.

“Greece will now move ahead with hope and reach out to Europe, and Europe is going to change,” Tsipras said Sunday night amid a throng of supporters. “The verdict is clear: We will bring an end to the vicious circle of austerity.”

The story of Greece over the past five years has been one of loss. From middle-class workers who have seen paychecks slashed, to young graduates who have no job prospects, to the lower middle classes pushed to the poverty line and forced to frequent food kitchens, nearly everyone has lost something here. Syriza calls it a humanitarian crisis perpetuated by the dogma of Europe-imposed austerity.

Tsipras has vowed to turn the tide, creating 300,000 new jobs, raising the minimum wage, and bringing back collective bargaining to the country. Those promises resonated throughout working class neighborhoods like Ilion, which sits in the southwest corner of the capital and has shifted sharply toward Syriza. In the last elections, in 2012, it handed Syriza 37.17 of votes, up from 5.78 in 2009.

“Syriza can bring us back our dignity,” says supporter Ms. Roussou, who says when she and her husband moved from the village to the capital to give their two daughters an edge in life, “we thought they were going to live like princesses.” Instead, once a month they go to the municipality for free beans, pasta, sugar, and milk.

“We asked for oil for cooking, and they told us we were lucky to have this plate of food,” she says. “All we are asking for is better for our children.”

'Burning coals'

But no one knows whether Tsipras realistically can meet these demands.

Outgoing Prime Minister Antonis Samaras, of the center-right New Democracy, conceded defeat last night, saying he had moved Greece toward growth under nearly insurmountable conditions. “I received the country at the edge of a cliff,” he said. “I was asked to take burning coals into my hands, and I did it.”

He has argued that Tsipras’s campaign pledge to sit down with European creditors and renegotiate debt agreements is bound to fail – and take Greece back into an era of turbulence. But Syriza has said that the current terms are untenable and have brought no prosperity to Greece or any country forced to cut budgets in return for money from lenders.

Dimitris Charalambis, a professor of political science at the University of Athens, compares Greece’s position today with its creditors to that of Germany in 1919 under the Treaty of Versailles.

Still, despite Greece's troubles, Europe is not simply going to yield to Syriza’s demands, says Spyros Economides, the deputy director of the Hellenic Observatory at the London School of Economics. A new agreement for Greece would translate abroad as an admission of political failure. Helping Greece could also mean a rush of demands from other bailed-out economies. And granting a reprieve to the south is not politically viable in many northern European nations.

“[A deal] would have to be something so technical that it doesn’t really change the terms or principles of the arrangement but enough so that it makes some kind of difference [in Greece],” says Mr. Economides.

Is hope coming?

In the end, that kind of slow-moving solution might not be enough to satisfy Greek expectations, built around Syriza’s slogan that “Hope is coming."

In fact, for all the expectancy in Ilion, there is also A tentativeness. Some doubt that Syriza can live up to its promises. Local butcher Nickolas Andriakenas was doing a brisk business on a recent day, but says sales are down by nearly half as the crisis churns on. He thinks that Syriza is just “the same face on the other side of the card. They are going to be our next political victim.”

Down the street at a hair salon, Nelli Xenou, a divorced mother of two who is out of a job, says that Syriza is an unknown entity. “Things are not good but people know how they are going. Syriza is a risk that I personally wouldn't take,” she says.

But for Mr. Davos, and many of his neighbors, there is no risk, because there is nothing else left to lose. “Syriza is the only party that can lead us back to having a quality of life. I believe in them with all of my heart.”